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I wonder how to check availability property from CAP theorem. Consistency check is conceptually easy: if at least once somehow same query at the same time returns different results, then the system may be considered inconsistent (or under some circumstances eventually consistent).

But what about availability? If it takes 1 millisecond for the system to respond, it probably should be considered available. If 1 second for a huge query - probably also available. But what about 50 seconds for a simple query?.. Where is the threshold - how much time should the system take to respond in order to consider it unavailable?

Well, one possible threshold is to consider system unavailable only if it throws some error immediately or doesn't respond at all. But with such definition we may consider available any system that lets the user wait for a long time until all inconsistencies and partitions are resolved.

So my questions are:

1) How do we check if system satisfies availability property as defined in CAP theorem?

2) How do we distinguish the following cases:

  • System is available, but it may take 10 minutes to process some huge query.
  • Actually system is not available, but there is some wrapper (user calls it instead of the original system) that each time when original system is not available simply waits until it becomes, so to the outside user it looks like the system is available and is simply processing the query.
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This is indeed a concern for those building real-world applications - how does one measure "availability" - not the binary property discussed in the CAP theorem, but the experience for users of the system.

There is industry agreement around this concern, and a standardized method of measuring it applicable to all systems. (Note: as stated in the comments, this is a separate concept from the theoretical concept of availability, which is analyzed from an algorithm, or perhaps from a simulation of a system.)

The Apdex method assumes you have a definition of "satisfied service" at some response time. Let's say you consider a sub-1-second response time to satisfactory to define "available." Then, by convention, "tolerable" service is 4 times the target time: in our case, a response time from 1 to 4 seconds. Response times longer than 4 seconds are considered "frustrated."

Then, the Apdex score is the number of satisfied requests, plus half the number of tolerable requests, plus none of the frustrated requests (i.e. 0), all divided by the total number of requests.

For example, if you had 100 total requests, and 30 of them were satisfied (< 1s), 50 were tolerable (>1s but <4s) and 20 were frustrated (>4s), the apdex score for your service for the period of time those requests were serviced would be (30+25+0)/100, or 0.55. (An apdex score, by virtue of being a ratio, is always between 0 and 1)

Fun fact: a bunch of businesses then teamed up to turn this quite simple idea into a fully-fledged business. If you are a business, you can pay the Apdex Alliance money so they can produce education, webinars, and blogs, as well as certify compliant business so they may use the Apdex name and logo(!)

(I am not affiliated with the Alliance. I just like standards.)

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https://en.wikipedia.org/wiki/CAP_theorem

"CAP is frequently misunderstood as if one had to choose to abandon one of the three guarantees at all times. In fact, the choice is really between consistency and availability for when a partition happens only; at all other times, no trade-off has to be made."

In other words, you are not measuring availability as a matter of "time" as you describe in your question -- it is a computer science property of how the system behaves when something gone wrong -- it is either available or not available -- that is a binary choice and nothing to do with timing or user access.

Once you have determined whether a system should be available or not (binary choice), then the question remains (your question 2) on how the implementation behaves -- and does it works slow vs not at all, but that is the difference between an erroneous implementation and a flawless one, and it is strictly not a computer science question any more than the question of "how do I produce bug-free code"

The CAP theorem is about the algo design of the database and not about writing code or the system that uses the database.

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  • $\begingroup$ Still the question remains is how we determine if the system satisfies availability property. $\endgroup$
    – Yurii
    Dec 31, 2016 at 4:43
  • $\begingroup$ Availability is binary, so you can reason about it -- it does not have to be measured to be determined $\endgroup$
    – Soren
    Dec 31, 2016 at 4:49
  • $\begingroup$ Seems wrong for me. It's like discussing soul while failing to name any functions that are performed by soul. Why do I ever need a concept if it is not bound to real world even approximately? $\endgroup$
    – Yurii
    Dec 31, 2016 at 5:00
  • $\begingroup$ It is connected to real world -- just not to the part you care about -- "Availability" is real in the sense of how to design an algo in computer science. When you set out to design a new system with a distributed architecture it is important to determine up front how the system should behave when something fails -- and that is what the CAP theorem is about -- it is not about how an end user sees the system in terms of responds times. $\endgroup$
    – Soren
    Dec 31, 2016 at 5:06
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    $\begingroup$ You use math and design the algo -- it is about algo design of the database and not about writing code or the system that uses the database $\endgroup$
    – Soren
    Dec 31, 2016 at 5:24

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